1/1x2+1/2x3+1/3x4+1/4x5+...+1/2009x2010

分类: 作业答案 • 2021-12-20 05:41:47

问题描述：

答

原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2009-1/2010
=1-1/2010
=2009/2010

答

解 1/1x2+1/2x3+1/3x4+1/4x5+...+1/2009x2010
=(1+1/1)+(1+1/2)+(1+1/3)+(1+1/4)+...+(1+1/2009)
=1x2009+2008/2009
=2009+2008/2009

答

1/1x2+1/2x3+1/3x4+1/4x5+...+1/2009x2010
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2009-1/2010
=1-1/2010
=2009/2010